A Simple Example - THE ACCOUNTING PRICE OF FOREIGN EXCHANGE

THE ACCOUNTING PRICE OF FOREIGN EXCHANGE

3.2 A Simple Example

Consider an investment project that increases the supply of foreign exchange by increasing exports, which are not subject to any foreign trade tax. To begin with a simple example, which will gradually become more complicated, let us initially assume that the supply of foreign exchange (exports) is completely inelastic with respect to price, that the exchange rate is determined by the market, that only final consumer goods are imported and that these goods are not produced domestically. The assumption of a fixed supply of foreign exchange will be abandoned in Section 3.5 and imported goods that compete with domestic production will be considered in Section 3.6. Thus, in Figure 3.1, SQ is the foreign exchange supply in the situation without the project, S, is that supply in the situation with the project and D is the demand for foreign Figure 3.1. The Foreign Exchange Market

foreign exchange

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exchange. This is used to import consumer goods a and b, which are not produced domestically, at international prices expressed in foreign exchange

CIFa and CIFb.

Assuming that the domestic transport and trade margins are nil, the domes-tic prices of such goods in the situation without the project will be

in which EER0 is the equilibrium exchange rate and ?; is the (ad valorem) import tariff. Since the adjustment to the additional supply of foreign ex-change will be made by means of a reduction in the (long term) equilibrium exchange rate to EER}, the domestic prices of a and b will be reduced to:

in which it is supposed that the international prices C/F, are constant in relation to small variations in the domestic demand of a country.

The compensating variation of the reduction in the price of the goods imported can be approximated by the increase in consumers' surplus (ACS), equal to the sum of the shaded areas in Figure 3.2(a) and (b). These areas can be approximated linearly as¹

that is, the reduction in the domestic value of the quantity that they consumed before the reduction in the exchange rate, plus their willingness to pay for additional consumption less what they actually pay for this consumption. It will now be useful to analyze each of the terms ACS is comprised of. Substi-tuting the expressions [3.1] and [3.2] in the first term of expressions [3.3]

yields the following:

1. Henceforth, to simplify the presentation, the areas below demand functions will always be approximated linearly.

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ACCOUNTING PRICE OF FOREIGN EXCHANGE

Figure 3.2. The Effects of an Increase in the Supply of Foreign Exchange on the Markets of Imported Goods

In turn, each of the above expressions can be broken down into two parts. The first is the reduction in Government revenue—by way of receipts from the import tariffs corresponding to imports in the situation without the project—

because of the reduction in the EER:

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The second part is the reduction in the exporters' revenue from the sale of the same quantity of foreign exchange (S0 in Figure 3.1) at a lower exchange rate:

The second term of expression [3.3] is willingness to pay for the additional quantity of goods a and b, which expresses the maximum quantity of other goods that the consumers would be prepared to forgo rather than do without such quantities. In this sense, this is not an actual income flow but a measure of income equivalent to such quantities. Finally, what is paid by the con-sumers for additional consumption

can be broken down by replacing the prices by expressions [3.2]. From this we see that what the consumers pay is equal to what the project receives from the sale of foreign exchange S\ — So generated by exports, equal to the value of the additional imports before taxes

plus the increase in receipts from import tariffs by the Government

A summary of the direct effects of the additional supply of foreign exchange appears in Table 3.1.

It is now possible to interpret the information contained in this table from two points of view: (a) that of the potential compensation criterion; and (b) that of the distributional value judgment assigning equal weights to all income changes. From the perspective of the potential compensation criterion, what we want to know is whether the additional income (effective or equivalent) received by those who benefit is sufficient to compensate the losers and leave a remainder. To do this, it is necessary to examine the table column by column. The first contains the sum of the CVs of the consumers benefiting from the effect of the greater supply of foreign exchange on consumer goods prices, an effect that, strictly speaking, ought to be subdivided into one

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Table 3.1. Direct Effects of the Increase in the Availability of Foreign Exchange

Change in the market value of the quantity consumed without the project Consumers' willingness to pay

Paid by the consumers Total

Consumers CIFa(EER0EERi)(\+ta)a0

I(pl+pl)(a,a₀)

C/F8ff/M1+4)(aiao) Change in consumers'

surplus

Project

CIFtEERfaad + Income from project +

Other Exporters

CIFa(EER0EERi)a0

Change in exporters' + income

Government

CIFa(EER0EERi)taa0

CIFaEER,ta(a,a0) Change in Government =

revenue

Total

I(p°a+pl}(a,a0)

Consumers' willingness to pay

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column for each consumer.² In other words, the total in the first column is the reduction in the income of the consumers, which would leave them at the same level of welfare as before the increase in the supply of foreign exchange (fall in the price of consumer goods). The second column records the project's revenue from the sale of exported goods. As the excess supply of foreign exchange causes a reduction in the EER, the remaining exporters see their incomes reduced by the extent shown in the third column. The fourth column shows the changes in tax revenue brought about by the project. Although the sign of the net effect on the Government is not defined, we will assume that it is positive.³

Consequently, there are three groups of gainers (the consumers, the project and the Government) whose additional income must be enough to compensate the losers (exporters) and leave a remainder to compensate the loss implicit in the project costs, which are not shown in Table 3.1. As can be seen in this table, the balance in question is the willingness to pay for the consumption made possible by the increase in the supply of foreign exchange. This sum is the income remaining after the (potential) compensation of those affected by the increase in the supply of foreign exchange, available to compensate those who are net losers as a result of the project costs. Thus, valuing the additional foreign exchange according to willingness to pay for the consumption which it makes possible ensures that the potential compensation criterion is complied with for those affected by the additional supply of foreign exchange. Since the compensation is only potential, this valuation is all that is required by the application of the potential Pareto improvement criterion.

The same result can be achieved by assigning the same weight to all mar-ginal income changes. In fact, this value judgment allows the columns in Table 3.1 to be added up horizontally. Thus, for example, in the first row, the gain by consumers is equal to the loss of the remaining exporters and the Government. As a result, the respective net effect on total welfare is nil. The net result of the horizontal sum of the columns is willingness to pay for the consumption made possible by the increase in the foreign exchange supply.

We may therefore conclude that both from the point of view of the potential Pareto improvement criterion and from that of "efficiency analysis," the accounting price of foreign exchange is as follows:

Willingness to pay for the consumption made possible A RET by the additional foreign exchange (Si - S0) ArrtL =

Additional foreign exchange (S\ — 50)

2. The reader will recall that to add CVs, judgments are required concerning the "value" of changes in income for each consumer affected.

3. This is consistent with the approximation EER0 = EER\ which will be incorporated in the analysis later (see expressions [3.8] and [3.9]).

ACCOUNTING PRICE OF FOREIGN EXCHANGE

The fact that both approaches yield the same result is not surprising. In Chapter 1, we saw that both are based on the same distributional value judgment.

What has been explained so far enables us to write a simple formula for the accounting price of foreign exchange when the exchange rate adjusts the supply and demand of foreign exchange. In the simple example explained up to now, expression [3.3] shows that the sum of the compensating variations of the additional supply of foreign exchange will be the sum of the willingness to pay of each individual consumer for the additional consumption made possible.

Now defining

and substituting [3.1] in [3.4] we obtain

By rearranging the terms, the above expressions can be reduced to

and the accounting price of foreign exchange will be

But as foreign exchange S, - S0 is used entirely to import quantities Aa and Afc,

Substituting [3.5] and [3.7] in [3.6] the accounting price of foreign exchange will be

If now we consider that normally the increase in the supply of foreign ex-change generated by a project has a minimum influence on the exex-change rate, we can say that for all practical purposes,

and expression [3.8] can be written as

However, the formula for the APFE is normally expressed as the relation between this accounting price and its market price (the HER). By calling this relation the accounting price ratio of foreign exchange (APRFE) we obtain

Generalizing expression [3.10] for n imported consumer goods m, we obtain

in which

is the share of each good / in additional imports. It should be pointed out that the weights <p{ refer to the additional imports generated exclusively by the

ACCOUNTING PRICE OF FOREIGN EXCHANGE

change in the exchange rate brought about by the increase in the supply of foreign exchange.⁴ Consequently, they cannot be estimated by simply com-paring the lists of imports between two periods since the Aw, thus observed incorporate the effect of income changes.

The reader will recognize the expression [3.11] as the traditional formula for the APRFE as presented in UNIDO (1972) or Harberger (1973), except that in these two works (1 + ?,) is replaced by a more general expression in order to allow for other forms of protection to be included such as an import quota, sold at a domestic price determined by the market and which will be expanded in accordance with the increase in the supply of foreign exchange.

If, for example, imports were subject to a domestic "sales" tax of -tj, the formula for the foreign exchange accounting price ratio would be

Elsewhere, the same expression [3.11] is shown in terms of the price elasticity of the demand functions of imported goods.

3.3 Income Transfers Generated by an Additional Supply of Exports

Im Dokument Beneﬁts and Beneﬁciaries: An Introduction to Estimating Distributional Eﬀects in Cost-Beneﬁt Analysis (Second Edition) (Seite 47-55)